A new actuator system to drive the rolling motion of a CNT on a graphene is investigated with the molecular dynamics simulation. The strain gradient field induced by the actuator system can be effectively used to realize the continuous and steady rolling of the CNT. Variations of the potential energy, the kinetic one, as well as the motion of the CNT is comprehensively studied for both cases without defects and those with defects. Effects of both the parameters of the CNT and vacancy defects of the graphene are discussed. It is interesting to find that a single defect results in small fluctuation of the CNT’s motion. However, multiple defects may lead to a serious deflection of the movement of the CNT, even failure of the actuator system. These results should be useful for the promising design of nanoscale transportation and functional surfaces.